The use of abstract logic and symbol manipulation as opposed to empirical observation.

simple past tense and past participle of algebraize

Third-person singular simple present indicative form of algebraize

(transitive) To perform by algebra; to reduce to algebraic form.

present participle of algebraize

(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

(algebra) A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3.

(algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.

of, or relating to linear algebra

(mathematics) A branch of mathematics that studies algebraic varieties (solution sets of polynomial equations) and their generalisations, using techniques from both algebra (chiefly commutative algebra) and geometry.